{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "134e7f9d",
   "metadata": {},
   "source": [
    "# Demo 3: Grid"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2571d531",
   "metadata": {},
   "source": [
    "One important feature of KANs is that they embed splines to neural networks. However, splines are only valid for approximating functions in known bounded regions, while the range of activations in neural networks may be changing over training. So we have to update grids properly according to that. Let's first take a look at how we parametrize splines. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2075ef56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'B_i(x)')"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kan.spline import B_batch\n",
    "import torch\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# consider a 1D example.\n",
    "# Suppose we have grid in [-1,1] with G intervals, spline order k\n",
    "G = 5\n",
    "k = 3\n",
    "grid = torch.linspace(-1,1,steps=G+1)[None,:]\n",
    "\n",
    "# and we have sample range in [-1,1]\n",
    "x = torch.linspace(-1,1,steps=1001)[None,:]\n",
    "\n",
    "basis = B_batch(x, grid, k=k)\n",
    "\n",
    "for i in range(G+k):\n",
    "    plt.plot(x[0].detach().numpy(), basis[0,i,:].detach().numpy())\n",
    "    \n",
    "plt.legend(['B_{}(x)'.format(i) for i in np.arange(G+k)])\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('B_i(x)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75af662c",
   "metadata": {},
   "source": [
    "There are $G+k$ B-spline basis. The function is a linear combination of these bases $${\\rm spline}(x)=\\sum_{i=0}^{G+k-1} c_i B_i(x).$$ We don't need worry about the implementation since it's already built in KAN. But let's check if KAN is indeed implementing this. We initialize a [1,1] KAN, which is simply a 1D spline."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4369a310",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.1382, grad_fn=<MeanBackward0>)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from kan import KAN\n",
    "\n",
    "model = KAN(width=[1,1], grid=G, k=k)\n",
    "# obtain coefficients c_i\n",
    "model.act_fun[0].coef\n",
    "assert(model.act_fun[0].coef[0].shape[0] == G+k)\n",
    "\n",
    "# the model forward\n",
    "model_output = model(x[0][:,None])\n",
    "\n",
    "# spline output\n",
    "spline_output = torch.einsum('i,ij->j',model.act_fun[0].coef[0], basis[0])[:,None]\n",
    "\n",
    "torch.mean((model_output - spline_output)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82150587",
   "metadata": {},
   "source": [
    "They are not the same, what's happening? We want to remind that we model the activation function to have two additive parts, a residual function $b$(x) plus the spline function, i.e., $$\\phi(x)={\\rm scale\\_base}*b(x)+{\\rm scale\\_sp}*{\\rm spline}(x),$$ and by default $b(x)={\\rm silu}(x)=x/(1+e^{-x})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7d76a3c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0., grad_fn=<MeanBackward0>)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# residual output\n",
    "residual_output = torch.nn.SiLU()(x[0][:,None])\n",
    "scale_base = model.act_fun[0].scale_base\n",
    "scale_sp = model.act_fun[0].scale_sp\n",
    "torch.mean((model_output - (scale_base * residual_output + scale_sp * spline_output))**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d72e076",
   "metadata": {},
   "source": [
    "What if my grid does not match my data? For example, my grid is in [-1,1], but my data is in [10,10] or [-0.5,0.5]. Use update_grid_from_sample to adjust grids to samples. This grid update applies to all splines in all layers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "46717e8b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter containing:\n",
      "tensor([[-1.0000, -0.6000, -0.2000,  0.2000,  0.6000,  1.0000]])\n",
      "Parameter containing:\n",
      "tensor([[-10.0100,  -6.0060,  -2.0020,   2.0020,   6.0060,  10.0100]])\n"
     ]
    }
   ],
   "source": [
    "model = KAN(width=[1,1], grid=G, k=k)\n",
    "print(model.act_fun[0].grid) # by default, the grid is in [-1,1]\n",
    "x = torch.linspace(-10,10,steps = 1001)[:,None]\n",
    "model.update_grid_from_samples(x)\n",
    "print(model.act_fun[0].grid) # now the grid becomes in [-10,10]. We add a 0.01 margin in case x have zero variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "de04db15",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter containing:\n",
      "tensor([[-1.0000, -0.6000, -0.2000,  0.2000,  0.6000,  1.0000]])\n",
      "Parameter containing:\n",
      "tensor([[-0.5100, -0.3060, -0.1020,  0.1020,  0.3060,  0.5100]])\n"
     ]
    }
   ],
   "source": [
    "model = KAN(width=[1,1], grid=G, k=k)\n",
    "print(model.act_fun[0].grid) # by default, the grid is in [-1,1]\n",
    "x = torch.linspace(-0.5,0.5,steps = 1001)[:,None]\n",
    "model.update_grid_from_samples(x)\n",
    "print(model.act_fun[0].grid) # now the grid becomes in [-10,10]. We add a 0.01 margin in case x have zero variance"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e418ca2c",
   "metadata": {},
   "source": [
    "Uniform grid or non-uniform? We consider two options: (1) uniform grid; (2) adaptive grid (based on sample distribution) such that there are (rougly) same number of samples in each interval. We provide a parameter grid_eps to interpolate between these two regimes. grid_eps = 1 gives (1), and grid_eps = 0 gives (0). By default we set grid_eps = 1 (uniform grid). There could be other options but it is out of our scope here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d2c4f636",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter containing:\n",
      "tensor([[-1.0000, -0.6000, -0.2000,  0.2000,  0.6000,  1.0000]])\n",
      "Parameter containing:\n",
      "tensor([[-3.4896, -2.1218, -0.7541,  0.6137,  1.9815,  3.3493]])\n"
     ]
    }
   ],
   "source": [
    "# uniform grid\n",
    "model = KAN(width=[1,1], grid=G, k=k)\n",
    "print(model.act_fun[0].grid) # by default, the grid is in [-1,1]\n",
    "x = torch.normal(0,1,size=(1000,1))\n",
    "model.update_grid_from_samples(x)\n",
    "print(model.act_fun[0].grid) # now the grid becomes in [-10,10]. We add a 0.01 margin in case x have zero variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b9b354c6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter containing:\n",
      "tensor([[-1.0000, -0.6000, -0.2000,  0.2000,  0.6000,  1.0000]])\n",
      "Parameter containing:\n",
      "tensor([[-3.4796, -0.8529, -0.2272,  0.2667,  0.8940,  3.3393]])\n"
     ]
    }
   ],
   "source": [
    "# adaptive grid based on sample distribution\n",
    "model = KAN(width=[1,1], grid=G, k=k, grid_eps = 0.)\n",
    "print(model.act_fun[0].grid) # by default, the grid is in [-1,1]\n",
    "x = torch.normal(0,1,size=(1000,1))\n",
    "model.update_grid_from_samples(x)\n",
    "print(model.act_fun[0].grid) # now the grid becomes in [-10,10]. We add a 0.01 margin in case x have zero variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f7b8f994",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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